Coordinates

Problem 1

Find the line equation through the origin with the same slope as the line between points $A(1,5)$ and $B(2,-3)$ .

See Solution

Problem 2

Find the focus of the parabola $x = y^{2} + 4y + 10$ . Choose from: $(-6.25,2)$ , $(-2,6.25)$ , $(6.25,-2)$ , $(2,6.25)$ .

See Solution

Problem 3

Identify the point that does not lie on the line formed by 3 of the following points: $(-2,-3)$ , $(3,2)$ , $(-1,0)$ , $(-3,-4)$ .

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Problem 4

Find the line equation through points (-2,1) and (1,-2). Options: a) $y=x-1$ , b) $y=x+1$ , c) $y=-2x+1$ , d) $y=1-x$ , e) $y=-x-1$ .

See Solution

Problem 5

Find the distance between points $(-1,2)$ and $(3,4)$ . Options: a) 5 b) $\sqrt{8}$ c) $\sqrt{10}$ d) $\sqrt{20}$ e) $\sqrt{40}$ .

See Solution

Problem 6

Identify the quadrilateral formed by the points $(-5,0),(0,4),(5,0),(0,-4)$ . Options: A. Trapezoid B. Rhombus C. Square D. Rectangle.

See Solution

Problem 7

Calculate the distance $d$ between points $A(11,-5)$ and $B(1,7)$ .

See Solution

Problem 8

Dalam Rajah 5, cari (a) titik tengah garis $P Q$ , (b) panjang $Q R$ untuk trapezium PQRS dengan P(-2,4), Q(4,6), R(9,1).

See Solution

Problem 9

Identify the quadrilateral formed by the points (0,0), (0,4), (8,4), (8,0). Options: A. Square B. Trapezoid C. Rectangle D. Rhombus.

See Solution

Problem 10

Find the maximum value of $b$ for the point $(a,b)$ satisfying the inequalities: $y \leq -15x + 3000$ and $y \leq 5x$ .

See Solution

Problem 11

Find the maximum value of $b$ for the point $(a, b)$ that satisfies the inequalities $y \leq -15x + 3000$ and $y \leq 5x$ .

See Solution

Problem 12

מצא את הגרף של הפונקציה $f(x)=\sqrt{3-x}$ .

See Solution

Problem 13

Find the x-intercept of the equation $3x + 4y = 8$ .

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Problem 14

Find the perimeter of Central Park, given vertices at $(-1.25,-0.25)$ , $(-1.25,0.25)$ , and $(1.25,0.25)$ . Show your work.

See Solution

Problem 15

What is the initial height of a tennis ball dropped from a height of $176.4$ cm at time $t=0$ ?

See Solution

Problem 16

Maximize $Z=3x+4y$ graphically with constraints: $x+y \leq 4$ , $x \geq 0$ , $y \geq 0$ .

See Solution

Problem 17

Find the coordinates of point $S$ in parallelogram $P Q R S$ with $P(-1,3)$ , $Q(-2,-3)$ , $R(1,0)$ . Also, find the equation of the perpendicular bisector of $P R$ and determine if $P Q R S$ is a rhombus.

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Problem 18

Find the equation of the line through the points $(-6, 3)$ and $(5, 8.5)$ . Choose from the options: a. $2y + x = 12$ , b. $y + 2x = -12$ , c. $y - \frac{1}{2}x = 6$ , d. $y - 2x = -9$ .

See Solution

Problem 19

Find the equation of line $O A$ , show $A$ is at $(16,-8)$ , and calculate the area of trapezium $O A B C$ .

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Problem 20

Find the equation of the line through points $(-6, 6)$ and $(4, -7\frac{1}{3})$ . Choose the correct option.

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Problem 21

Find the $y$ intercept $r$ of the line through points $(-3, \frac{5}{2})$ and $(4, -1)$ . What is $r$ ?

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Problem 22

One vertex of a square is at the origin, with others at $(-3,0)$ and $(0,-3)$ . Find the fourth vertex coordinates.
Find the perimeter and area of a rectangle with vertices at $(3,-2),(-2,-2),(-2,4)$ , and $(3,4)$ .

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Problem 23

Find the area of the triangle with vertices $(4,4)$ , $(4,0)$ , and $(0,0)$ by counting whole and half squares. 8 sq. units. Which quadrant is the point $(-3,2)$ in? Second.

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Problem 24

Find the length of a segment with endpoints at $(-1, 11)$ and $(4, 5)$ .

See Solution

Problem 25

Determine the location of the point $(-3,4)$ in the coordinate plane.

See Solution

Problem 26

Find the perimeter of Central Park, given vertices at $(-1.25,-0.25)$ , $(-1.25,0.25)$ , and $(1.25,0.25)$ .

See Solution

Problem 27

Determine the quadrant for a point with positive coordinates $(x > 0, y > 0)$ .

See Solution

Problem 28

Christopher's fence is rectangular, with length $2 \mathrm{ft}$ longer than width. Points are $S(1, -2)$ , $R(6, -2)$ , $P(1, 8)$ , $Q(6, 4)$ .

See Solution

Problem 29

Zeichne den Graphen für Anettes Inlinerfahrt: Ampelhalt, steiniger Weg, Auto vorlassen, dann Ankunft.

See Solution

Problem 30

Der Bus fährt um 8.05 Uhr ab. a) Zeichne den Graphen. b) Wann ist die Endstation erreicht? c) Wie lang ist die Strecke?

See Solution

Problem 31

Find point $B$ on line segment $AC$ where $A(6,-6)$ , $C(-6,-2)$ , and $AB=\frac{3}{4}AC$ .

See Solution

Problem 32

Determine the equation of the plane through points $A(1, 0, 0)$ , $B(0, -3, 1)$ , and $C(2, -2, 0)$ .

See Solution

Problem 33

Find the equation of line $PQ$ for quadrilateral $PQRS$ with points $P(-2,1)$ , $Q(1,-5)$ , and $S(2,3)$ .

See Solution

Problem 34

Gegeben sind die Punkte A(2,-3,0), B(2,2,0), C(-1,2,0) und E(2,-3,5) eines Quaders. Finde die anderen Eckpunkte und berechne die Diagonale $\overline{A G}$ .

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Problem 35

Graph the line given by the equation $y=x-2$ .

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Problem 36

Gegeben sind die Punkte A(2|-3|0), B(2|2|0), C(-1|2|0) und E(2|-3|5) eines Quaders. Finde die anderen Eckpunkte und die Länge der Diagonale $\overline{A G}$ .

See Solution

Problem 37

Find the equation of the line through $(-3,4)$ with an undefined slope.

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Problem 38

Find the equation of the line passing through $(-1,-2)$ with a slope of $1$ .

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Problem 39

Find the equation of the line through $(4,1)$ that is perpendicular to $y=-\frac{4}{3}x+4$ .

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Problem 40

Find the vertical and horizontal changes between points $(2.5,1)$ and $(5,2)$ . Then, calculate the slope using these changes.

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Problem 41

Trova il punto di intersezione tra il piano $4x - y + 2z - 3 = 0$ e la retta $x = -2 - 2t$ , $y = 1 + t$ , $z = -5 - t$ .

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Problem 42

Scrivi l'equazione della retta $r$ che passa per $P(1, 0, -1)$ e è parallela ai piani $x+2y+z+3=0$ e $2x+y-z+1=0$ . $[x-1=-y=z+1]$

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Problem 43

Find the slope of the line through points $(8,2)$ and $(12,-10)$ . What is $\mathrm{m}$ ? $\mathrm{m}=[?]$

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Problem 44

Find the missing input for the slope formula $m=\frac{0-[?]}{-1-3}$ using points $(-1,-2)$ and $(3,0)$ . Options: A. -2, B. -1, C. 0, D. 3.

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Problem 45

Find the slope of the line through the points (5,3) and (8,-6). $\mathrm{m}=[?]$

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Problem 46

Find the slope of the line through points $(12,3)$ and $(6,1)$ . Simplify: Slope $=[?] \frac{[]}{[]}$

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Problem 47

Find the slope of the line through points $(-9,-2)$ and $(5,1)$ . Slope $=\frac{[?]}{[]}$ .

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Problem 48

Find point $P$ on line segment $\overline{A F}$ where the ratio $AP:PF = 1:3$ . Determine the location of $P$ on the number line.

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Problem 49

Find the slope of the line for the points (1,10) to (2,20) and for (1,10) to (5,50). What does it represent?

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Problem 50

Trace the level sets for these functions:
1. $f(x, y)=x-y$
2. $f(x, y)=xy$
3. $f(x, y)=\arcsin\left(\frac{y}{x}\right)$
4. $f(x, y)=e^{y-x^{2}}$
5. $f(x, y, z)=x^{2}-2x+y^{2}+z^{2}+1$

See Solution

Problem 51

Find the distance from the Tax Office at $(-1.5,-1)$ to the Gas Station at $(3,4)$ , rounded to the nearest tenth.

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Problem 52

Calculate the distance between points A(4,9) and B(2,-3) using the formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

See Solution

Problem 53

Calculate the distance between points A(4,9) and C(9,0) using the formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

See Solution

Problem 54

Calculate the distance between points B(2,-3) and C(9,0) using the formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

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Problem 55

Find the distances between points A(4,9), B(-2,-3), and C(0,0). Round to the nearest tenth.

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Problem 56

Find the $x$ intercept $r$ of the line through points $(2, -3)$ and $(4, 4)$ . What is $r$ ?

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Problem 57

Graph the line defined by the equation $y + 3 = -2(x - 4)$ .

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Problem 58

Find the coordinates of the endpoint of $\overline{X Y}$ if one endpoint is $(8,-10)$ and the midpoint is at the origin.

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Problem 59

Find the midpoint coordinates of segments with endpoints: M(7,1) & N(4,-1), J(5,-3) & K(3,-8).

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Problem 60

جد ارتفاع الجسر عند النقطة التي تبعد 6 م عن بدايته، إذا كانت المسافة بين قاعدتيه 24 م وارتفاعه 9 م.

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Problem 61

Rhianna claims different functions can share $x$ -intercepts $(-5,0),(2,0),(6,0)$ , domain $[-5,7]$ , and range $[-4,10]$ . Can you find examples?

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Problem 62

Find the midpoint of points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ . Which option is correct? A, B, C, D, or E?

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Problem 63

Find the midpoint of the segment with endpoints $(-5,2)$ and $(-2,10)$ .

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Problem 64

Find the midpoint of the segment with endpoints $(6,7)$ and $(2,1)$ .

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Problem 65

Find the coordinates of point $B$ if the midpoint $M(-2,-2)$ and point $A(-3,-6)$ are given.

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Problem 66

Find the coordinates of point $B$ if the midpoint $M(5,-3)$ and point $A(3,-8)$ are given.

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Problem 67

What are the conditions for points in the third quadrant? Where can points with same or opposite signs lie?

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Problem 68

Label the second quadrant and answer: a. Give one point's coordinates in the second quadrant. b. Describe the coordinates for points there.

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Problem 69

Identify the quadrants where an ordered pair has coordinates with the same sign and where they are opposites.

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Problem 70

Calculate the distance between points $(2,-10)$ and $(13,18)$ . Provide exact and rounded to 1 decimal place.

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Problem 71

Find the equation of line $AB$ that passes through points $A(0,-4)$ and $B(6,2)$ . Options are: $y-4=3x$ , $y-2=3(x-6)$ , $y+4=x$ , $y+6=x-2$ .

See Solution

Problem 72

Find the midpoint of the line segment with endpoints $Q(6,3)$ and $R(2,5)$ . Write coordinates as decimals or integers: $M=$

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Problem 73

Find the midpoint of the line segment with endpoints $P(0,9)$ and $Q(10,7)$ . Write coordinates as decimals or integers.

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Problem 74

Find the midpoint $M$ of the line segment with endpoints $G(5,4)$ and $H(7,4)$ . Write $M$ as decimals or integers. $M=$

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Problem 75

Plot the points $(-4,1)$ and $(1,-1.5)$ on the coordinate plane. Click to add or remove points.

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Problem 76

Graph $f(x)=\frac{|x+3|}{x+3}$ for $x$ in the range $[-4,4]$ .

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Problem 77

Calculate the slope of the line through points $(-2,1)$ and $(2,2)$ . Note if it's vertical or horizontal.

See Solution

Problem 78

Graph the line given by the equation $y=-\frac{1}{3} x-2$ .

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Problem 79

Find the missing endpoint $D$ if $E(4,3)$ is the midpoint of $\overline{D F}$ with $F(5,8)$ . Options: a) $D(-1,-5)$ b) $D(6,13)$ c) $D(3,-2)$ d) $D(0.5,5.5)$

See Solution

Problem 80

Calculate the distance between points $G(-5,4)$ and $H(2,6)$ in simplest exact form.

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Problem 81

Calculate the slope of the line through the points $(-2,1)$ and $(-3,1)$ .

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Problem 82

Graph the line through the point $(-4,-3)$ with slope $m=4$ .

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Problem 83

Graph the line through the point $(-3,-5)$ with a slope of $m=3$ .

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Problem 84

Find the distance and bearing from Corpus Christi to the Coast Guard cutter after it travels at 30 knots for 4 hours on given courses.

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Problem 85

Graph the distance from home after $x$ hours for a trip to a park 20 miles away at $40 \mathrm{mph}$ , 2 hours at the park, then return at $20 \mathrm{mph}$ .

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Problem 86

Find the coordinates of a station such that the distance from Rolesville $R(1,2)$ to the station and from the station to Townsend $T(8,23)$ is in a $3:4$ ratio.

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Problem 87

Sofia paraglides from a cliff 840 m high, landing 321 m away. When her travel ratio is $1: 2$ , find her distance from the cliff.

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Problem 88

Find the midpoint of the segment with endpoints $(5,11)$ and $(3,1)$ .

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Problem 89

Find the midpoint of the segment with endpoints $(5,11)$ and $(3,1)$ .

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Problem 90

Find the missing endpoint $C$ if $B$ is the midpoint of $\overline{A C}$ , given $A(1,7)$ and $B(-3,1)$ .

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Problem 91

Find the missing endpoint $C$ if $B$ is the midpoint of $\overline{A C}$ with $A(-4,2)$ and $B(6,-1)$ .

See Solution

Problem 92

Find the slope of a line parallel to one that passes through $(2,3)$ and $(3,2)$ .

See Solution

Problem 93

Find the distance between the points $(1,2)$ and $(4,6)$ using the distance formula.

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Problem 94

Find the equation of the line perpendicular to $2 x=4 y-8$ that passes through the point $(1,2)$ .

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Problem 95

Find the midpoint of the line segment between the points $(-2,4)$ and $(2,6)$ .

See Solution

Problem 96

Find the distance between the points $(3,1)$ and $(7,7)$ using the distance formula.

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Problem 97

Find the midpoint of the segment between the points $(-7,5)$ and $(7,7)$ .

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Problem 98

Find the equation of the locus of point $P(x, y)$ such that the distances to points $S(4,6)$ and $R(12,6)$ are equal: $|P S|=|P R|$ .

See Solution

Problem 99

Find the intercepts of the equation $9 x^{2}+4 y^{2}=36$ . A. List them as ordered pairs. B. Or state there are none.

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Problem 100

Calculate the slope of the line through the points $(0,3)$ and $(6,0)$ .

See Solution

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Coordinates

Problem 1

Find the line equation through the origin with the same slope as the line between points A(1,5) A(1,5) A(1,5) and B(2,−3) B(2,-3) B(2,−3).

Problem 2

Find the focus of the parabola x=y2+4y+10 x = y^{2} + 4y + 10 x=y2+4y+10. Choose from: (−6.25,2) (-6.25,2) (−6.25,2), (−2,6.25) (-2,6.25) (−2,6.25), (6.25,−2) (6.25,-2) (6.25,−2), (2,6.25) (2,6.25) (2,6.25).

Problem 3

Identify the point that does not lie on the line formed by 3 of the following points: (−2,−3)(-2,-3)(−2,−3), (3,2)(3,2)(3,2), (−1,0)(-1,0)(−1,0), (−3,−4)(-3,-4)(−3,−4).

Problem 4

Find the line equation through points (-2,1) and (1,-2). Options: a) y=x−1y=x-1y=x−1, b) y=x+1y=x+1y=x+1, c) y=−2x+1y=-2x+1y=−2x+1, d) y=1−xy=1-xy=1−x, e) y=−x−1y=-x-1y=−x−1.

Problem 5

Find the distance between points (−1,2)(-1,2)(−1,2) and (3,4)(3,4)(3,4). Options: a) 5 b) 8\sqrt{8}8​ c) 10\sqrt{10}10​ d) 20\sqrt{20}20​ e) 40\sqrt{40}40​.

Problem 6

Identify the quadrilateral formed by the points (−5,0),(0,4),(5,0),(0,−4)(-5,0),(0,4),(5,0),(0,-4)(−5,0),(0,4),(5,0),(0,−4). Options: A. Trapezoid B. Rhombus C. Square D. Rectangle.

Problem 7

Calculate the distance ddd between points A(11,−5)A(11,-5)A(11,−5) and B(1,7)B(1,7)B(1,7).

Problem 8

Dalam Rajah 5, cari (a) titik tengah garis PQP QPQ, (b) panjang QRQ RQR untuk trapezium PQRS dengan P(-2,4), Q(4,6), R(9,1).

Problem 9

Identify the quadrilateral formed by the points (0,0), (0,4), (8,4), (8,0). Options: A. Square B. Trapezoid C. Rectangle D. Rhombus.

Problem 10

Find the maximum value of bbb for the point (a,b)(a,b)(a,b) satisfying the inequalities: y≤−15x+3000y \leq -15x + 3000y≤−15x+3000 and y≤5xy \leq 5xy≤5x.

Problem 11

Find the maximum value of bbb for the point (a,b)(a, b)(a,b) that satisfies the inequalities y≤−15x+3000y \leq -15x + 3000y≤−15x+3000 and y≤5xy \leq 5xy≤5x.

Problem 12

מצא את הגרף של הפונקציה f(x)=3−xf(x)=\sqrt{3-x}f(x)=3−x​.

Problem 13

Find the x-intercept of the equation 3x+4y=83x + 4y = 83x+4y=8.

Problem 14

Find the perimeter of Central Park, given vertices at (−1.25,−0.25)(-1.25,-0.25)(−1.25,−0.25), (−1.25,0.25)(-1.25,0.25)(−1.25,0.25), and (1.25,0.25)(1.25,0.25)(1.25,0.25). Show your work.

Problem 15

What is the initial height of a tennis ball dropped from a height of 176.4176.4176.4 cm at time t=0t=0t=0?

Problem 16

Maximize Z=3x+4yZ=3x+4yZ=3x+4y graphically with constraints: x+y≤4x+y \leq 4x+y≤4, x≥0x \geq 0x≥0, y≥0y \geq 0y≥0.

Problem 17

Find the coordinates of point SSS in parallelogram PQRSP Q R SPQRS with P(−1,3)P(-1,3)P(−1,3), Q(−2,−3)Q(-2,-3)Q(−2,−3), R(1,0)R(1,0)R(1,0). Also, find the equation of the perpendicular bisector of PRP RPR and determine if PQRSP Q R SPQRS is a rhombus.

Problem 18

Find the equation of the line through the points (−6,3)(-6, 3)(−6,3) and (5,8.5)(5, 8.5)(5,8.5). Choose from the options: a. 2y+x=122y + x = 122y+x=12, b. y+2x=−12y + 2x = -12y+2x=−12, c. y−12x=6y - \frac{1}{2}x = 6y−21​x=6, d. y−2x=−9y - 2x = -9y−2x=−9.

Problem 19

Find the equation of line OAO AOA, show AAA is at (16,−8)(16,-8)(16,−8), and calculate the area of trapezium OABCO A B COABC.

Problem 20

Find the equation of the line through points (−6,6)(-6, 6)(−6,6) and (4,−713)(4, -7\frac{1}{3})(4,−731​). Choose the correct option.

Problem 21

Find the yyy intercept rrr of the line through points (−3,52)(-3, \frac{5}{2})(−3,25​) and (4,−1)(4, -1)(4,−1). What is rrr?

Problem 22

Problem 23

Find the area of the triangle with vertices (4,4)(4,4)(4,4), (4,0)(4,0)(4,0), and (0,0)(0,0)(0,0) by counting whole and half squares. 8 sq. units. Which quadrant is the point (−3,2)(-3,2)(−3,2) in? Second.

Problem 24

Find the length of a segment with endpoints at (−1,11)(-1, 11)(−1,11) and (4,5)(4, 5)(4,5).

Problem 25

Determine the location of the point (−3,4)(-3,4)(−3,4) in the coordinate plane.

Problem 26

Find the perimeter of Central Park, given vertices at (−1.25,−0.25)(-1.25,-0.25)(−1.25,−0.25), (−1.25,0.25)(-1.25,0.25)(−1.25,0.25), and (1.25,0.25)(1.25,0.25)(1.25,0.25).

Problem 27

Determine the quadrant for a point with positive coordinates (x>0,y>0)(x > 0, y > 0)(x>0,y>0).

Problem 28

Christopher's fence is rectangular, with length 2ft2 \mathrm{ft}2ft longer than width. Points are S(1,−2)S(1, -2)S(1,−2), R(6,−2)R(6, -2)R(6,−2), P(1,8)P(1, 8)P(1,8), Q(6,4)Q(6, 4)Q(6,4).

Problem 29

Zeichne den Graphen für Anettes Inlinerfahrt: Ampelhalt, steiniger Weg, Auto vorlassen, dann Ankunft.

Problem 30

Der Bus fährt um 8.05 Uhr ab. a) Zeichne den Graphen. b) Wann ist die Endstation erreicht? c) Wie lang ist die Strecke?

Problem 31

Find point BBB on line segment ACACAC where A(6,−6)A(6,-6)A(6,−6), C(−6,−2)C(-6,-2)C(−6,−2), and AB=34ACAB=\frac{3}{4}ACAB=43​AC.

Problem 32

Determine the equation of the plane through points A(1,0,0)A(1, 0, 0)A(1,0,0), B(0,−3,1)B(0, -3, 1)B(0,−3,1), and C(2,−2,0)C(2, -2, 0)C(2,−2,0).

Problem 33

Find the equation of line PQPQPQ for quadrilateral PQRSPQRSPQRS with points P(−2,1)P(-2,1)P(−2,1), Q(1,−5)Q(1,-5)Q(1,−5), and S(2,3)S(2,3)S(2,3).

Problem 34

Gegeben sind die Punkte A(2,-3,0), B(2,2,0), C(-1,2,0) und E(2,-3,5) eines Quaders. Finde die anderen Eckpunkte und berechne die Diagonale AG‾\overline{A G}AG.

Problem 35

Graph the line given by the equation y=x−2y=x-2y=x−2.

Problem 36

Gegeben sind die Punkte A(2|-3|0), B(2|2|0), C(-1|2|0) und E(2|-3|5) eines Quaders. Finde die anderen Eckpunkte und die Länge der Diagonale AG‾\overline{A G}AG.

Problem 37

Find the equation of the line through (−3,4)(-3,4)(−3,4) with an undefined slope.

Problem 38

Find the equation of the line passing through (−1,−2)(-1,-2)(−1,−2) with a slope of 111.

Problem 39

Find the equation of the line through (4,1)(4,1)(4,1) that is perpendicular to y=−43x+4y=-\frac{4}{3}x+4y=−34​x+4.

Problem 40

Find the vertical and horizontal changes between points (2.5,1)(2.5,1)(2.5,1) and (5,2)(5,2)(5,2). Then, calculate the slope using these changes.

Find the line equation through the origin with the same slope as the line between points $A(1,5)$ and $B(2,-3)$ .

Find the focus of the parabola $x = y^{2} + 4y + 10$ . Choose from: $(-6.25,2)$ , $(-2,6.25)$ , $(6.25,-2)$ , $(2,6.25)$ .

Identify the point that does not lie on the line formed by 3 of the following points: $(-2,-3)$ , $(3,2)$ , $(-1,0)$ , $(-3,-4)$ .

Find the line equation through points (-2,1) and (1,-2). Options: a) $y=x-1$ , b) $y=x+1$ , c) $y=-2x+1$ , d) $y=1-x$ , e) $y=-x-1$ .

Find the distance between points $(-1,2)$ and $(3,4)$ . Options: a) 5 b) $\sqrt{8}$ c) $\sqrt{10}$ d) $\sqrt{20}$ e) $\sqrt{40}$ .

Identify the quadrilateral formed by the points $(-5,0),(0,4),(5,0),(0,-4)$ . Options: A. Trapezoid B. Rhombus C. Square D. Rectangle.

Calculate the distance $d$ between points $A(11,-5)$ and $B(1,7)$ .

Dalam Rajah 5, cari (a) titik tengah garis $P Q$ , (b) panjang $Q R$ untuk trapezium PQRS dengan P(-2,4), Q(4,6), R(9,1).

Find the maximum value of $b$ for the point $(a,b)$ satisfying the inequalities: $y \leq -15x + 3000$ and $y \leq 5x$ .

Find the maximum value of $b$ for the point $(a, b)$ that satisfies the inequalities $y \leq -15x + 3000$ and $y \leq 5x$ .

מצא את הגרף של הפונקציה $f(x)=\sqrt{3-x}$ .

Find the x-intercept of the equation $3x + 4y = 8$ .

Find the perimeter of Central Park, given vertices at $(-1.25,-0.25)$ , $(-1.25,0.25)$ , and $(1.25,0.25)$ . Show your work.

What is the initial height of a tennis ball dropped from a height of $176.4$ cm at time $t=0$ ?

Maximize $Z=3x+4y$ graphically with constraints: $x+y \leq 4$ , $x \geq 0$ , $y \geq 0$ .

Find the coordinates of point $S$ in parallelogram $P Q R S$ with $P(-1,3)$ , $Q(-2,-3)$ , $R(1,0)$ . Also, find the equation of the perpendicular bisector of $P R$ and determine if $P Q R S$ is a rhombus.

Find the equation of the line through the points $(-6, 3)$ and $(5, 8.5)$ . Choose from the options: a. $2y + x = 12$ , b. $y + 2x = -12$ , c. $y - \frac{1}{2}x = 6$ , d. $y - 2x = -9$ .

Find the equation of line $O A$ , show $A$ is at $(16,-8)$ , and calculate the area of trapezium $O A B C$ .

Find the equation of the line through points $(-6, 6)$ and $(4, -7\frac{1}{3})$ . Choose the correct option.

Find the $y$ intercept $r$ of the line through points $(-3, \frac{5}{2})$ and $(4, -1)$ . What is $r$ ?

Find the area of the triangle with vertices $(4,4)$ , $(4,0)$ , and $(0,0)$ by counting whole and half squares. 8 sq. units. Which quadrant is the point $(-3,2)$ in? Second.

Find the length of a segment with endpoints at $(-1, 11)$ and $(4, 5)$ .

Determine the location of the point $(-3,4)$ in the coordinate plane.

Find the perimeter of Central Park, given vertices at $(-1.25,-0.25)$ , $(-1.25,0.25)$ , and $(1.25,0.25)$ .

Determine the quadrant for a point with positive coordinates $(x > 0, y > 0)$ .

Christopher's fence is rectangular, with length $2 \mathrm{ft}$ longer than width. Points are $S(1, -2)$ , $R(6, -2)$ , $P(1, 8)$ , $Q(6, 4)$ .

Find point $B$ on line segment $AC$ where $A(6,-6)$ , $C(-6,-2)$ , and $AB=\frac{3}{4}AC$ .

Determine the equation of the plane through points $A(1, 0, 0)$ , $B(0, -3, 1)$ , and $C(2, -2, 0)$ .

Find the equation of line $PQ$ for quadrilateral $PQRS$ with points $P(-2,1)$ , $Q(1,-5)$ , and $S(2,3)$ .

Gegeben sind die Punkte A(2,-3,0), B(2,2,0), C(-1,2,0) und E(2,-3,5) eines Quaders. Finde die anderen Eckpunkte und berechne die Diagonale $\overline{A G}$ .

Graph the line given by the equation $y=x-2$ .

Gegeben sind die Punkte A(2|-3|0), B(2|2|0), C(-1|2|0) und E(2|-3|5) eines Quaders. Finde die anderen Eckpunkte und die Länge der Diagonale $\overline{A G}$ .

Find the equation of the line through $(-3,4)$ with an undefined slope.

Find the equation of the line passing through $(-1,-2)$ with a slope of $1$ .

Find the equation of the line through $(4,1)$ that is perpendicular to $y=-\frac{4}{3}x+4$ .

Find the vertical and horizontal changes between points $(2.5,1)$ and $(5,2)$ . Then, calculate the slope using these changes.

Trova il punto di intersezione tra il piano $4x - y + 2z - 3 = 0$ e la retta $x = -2 - 2t$ , $y = 1 + t$ , $z = -5 - t$ .

Scrivi l'equazione della retta $r$ che passa per $P(1, 0, -1)$ e è parallela ai piani $x+2y+z+3=0$ e $2x+y-z+1=0$ . $[x-1=-y=z+1]$

Find the slope of the line through points $(8,2)$ and $(12,-10)$ . What is $\mathrm{m}$ ? $\mathrm{m}=[?]$

Find the missing input for the slope formula $m=\frac{0-[?]}{-1-3}$ using points $(-1,-2)$ and $(3,0)$ . Options: A. -2, B. -1, C. 0, D. 3.

Find the slope of the line through the points (5,3) and (8,-6). $\mathrm{m}=[?]$

Find the slope of the line through points $(12,3)$ and $(6,1)$ . Simplify: Slope $=[?] \frac{[]}{[]}$

Find the slope of the line through points $(-9,-2)$ and $(5,1)$ . Slope $=\frac{[?]}{[]}$ .

Find point $P$ on line segment $\overline{A F}$ where the ratio $AP:PF = 1:3$ . Determine the location of $P$ on the number line.

Find the distance from the Tax Office at $(-1.5,-1)$ to the Gas Station at $(3,4)$ , rounded to the nearest tenth.

Calculate the distance between points A(4,9) and B(2,-3) using the formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

Calculate the distance between points A(4,9) and C(9,0) using the formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

Calculate the distance between points B(2,-3) and C(9,0) using the formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ .

Find the $x$ intercept $r$ of the line through points $(2, -3)$ and $(4, 4)$ . What is $r$ ?

Graph the line defined by the equation $y + 3 = -2(x - 4)$ .

Find the coordinates of the endpoint of $\overline{X Y}$ if one endpoint is $(8,-10)$ and the midpoint is at the origin.

Rhianna claims different functions can share $x$ -intercepts $(-5,0),(2,0),(6,0)$ , domain $[-5,7]$ , and range $[-4,10]$ . Can you find examples?

Find the midpoint of points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ . Which option is correct? A, B, C, D, or E?

Find the midpoint of the segment with endpoints $(-5,2)$ and $(-2,10)$ .

Find the midpoint of the segment with endpoints $(6,7)$ and $(2,1)$ .

Find the coordinates of point $B$ if the midpoint $M(-2,-2)$ and point $A(-3,-6)$ are given.

Find the coordinates of point $B$ if the midpoint $M(5,-3)$ and point $A(3,-8)$ are given.

Calculate the distance between points $(2,-10)$ and $(13,18)$ . Provide exact and rounded to 1 decimal place.

Find the equation of line $AB$ that passes through points $A(0,-4)$ and $B(6,2)$ . Options are: $y-4=3x$ , $y-2=3(x-6)$ , $y+4=x$ , $y+6=x-2$ .

Find the midpoint of the line segment with endpoints $Q(6,3)$ and $R(2,5)$ . Write coordinates as decimals or integers: $M=$

Find the midpoint of the line segment with endpoints $P(0,9)$ and $Q(10,7)$ . Write coordinates as decimals or integers.

Find the midpoint $M$ of the line segment with endpoints $G(5,4)$ and $H(7,4)$ . Write $M$ as decimals or integers. $M=$